A Constraint Logic Programming Algorithm for Modeling Dynamic Pricing

We extend Lemke's algorithm to solve a dynamic pricing problem. We identify an instance in which Lemke's algorithm fails to converge to an optimal solution (when an optimum does exist) and propose a constraint logic programming solution to this problem. We analyze the complexity of the extended Lemke's algorithm. Our analysis shows that, in the short term, dynamic pricing can be used to improve resource management efficiency. It is also shown that dynamic pricing can be used to manage the long-term behavior of demand.

[1]  Gabriel R. Bitran,et al.  An Application of Yield Management to the Hotel Industry Considering Multiple Day Stays , 1995, Oper. Res..

[2]  Andrew W. Moore,et al.  Reinforcement Learning: A Survey , 1996, J. Artif. Intell. Res..

[3]  Jeffrey O. Kephart,et al.  Dynamic pricing by software agents , 2000, Comput. Networks.

[4]  W. M. Kincaid,et al.  An inventory pricing problem , 1963 .

[5]  Martin Bichler,et al.  Applications of flexible pricing in business-to-business electronic commerce , 2002, IBM Syst. J..

[6]  Richard S. Sutton,et al.  Reinforcement Learning: An Introduction , 1998, IEEE Trans. Neural Networks.

[7]  Garrett J. van Ryzin,et al.  A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management , 1997, Oper. Res..

[8]  Samuel E. Bodily,et al.  A Taxonomy and Research Overview of Perishable-Asset Revenue Management: Yield Management, Overbooking, and Pricing , 1992, Oper. Res..

[9]  S. Kimes.  Yield management: A tool for capacity-considered service firms , 1989 .

[10]  Jeffrey I. McGill,et al.  Revenue Management: Research Overview and Prospects , 1999, Transp. Sci..

[11]  Shaul P. Ladany,et al.  Optimal cruise-liner passenger cabin pricing policy , 1991 .

[12]  R. Bellman.  Dynamic programming. , 1957, Science.

[13]  Soumyadip Ghosh,et al.  Bid Evaluation in Procurement Auctions with Piecewise Linear Supply Curves , 2005, J. Heuristics.

[14]  Soumyadip Ghosh,et al.  IBM Research Report Bid Evaluation in Procurement Auctions with Piece-Wise Linear Supply Curves , 2001 .

[15]  T C Botimer,et al.  Airline pricing and fare product differentiation: A new theoretical framework , 1999, J. Oper. Res. Soc..

[16]  Awi Federgruen,et al.  Combined Pricing and Inventory Control Under Uncertainty , 1999, Oper. Res..

[17]  Laura Palagi,et al.  A Mathematical Programming Approach for the Solution of the Railway Yield Management Problem , 1999, Transp. Sci..

[18]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[19]  C. E. Lemke,et al.  Bimatrix Equilibrium Points and Mathematical Programming , 1965 .

[20]  Peng-Sheng You,et al.  Dynamic Pricing in Airline Seat Management for Flights with Multiple Flight Legs , 1999, Transp. Sci..

[21]  Laura Wynter,et al.  Optimizing Proportionally Fair Prices , 2004, Telecommun. Syst..